Question

2. In the product of (4a3 + 5a2 – 11a) and (-15 + 3a – 7a2), the co-efficient of a4 is …………………… .

Answer 1

The only pairs that will give you some multiple of
`a^4` are:

`4a^3\cdot (3a),\quad 5a^2\cdot(-7a^2)`

their values are respectively

`12a^4,\quad -35a^4`

and their sum is
`-23a^4`

Answer 2

- 23

Explanation:

We could do this the long way and expand the whole product or note that the
`a^(4)` terms arise from the product of the a³ and a terms and the product of the a² and a² terms, that is

4a³ × 3a = 12
`a^(4)`

+ 5a² × - 7a² = - 35
`a^(4)`

Summing gives

12
`a^(4)` - 35
`a^(4)` = - 23
`a^(4)`

with coefficient - 23